Multiple Ratios Flashcards

All 7 cards in this deck

What are the steps to combine $A:B$ and $B:C$ into a single ratio $A:B:C$?
e.g. $A:B = 2:5$ and $B:C = 4:1$

1. Make the $B$ parts match — LCM of 5 and 4 is 20
2. Scale each ratio: $A:B = 8:20$ and $B:C = 20:5$
3. Combine: $A:B:C = 8:20:5$

What are the steps to solve a ratio problem when you are given the difference between two shares instead of the total?
e.g. $R:M:I = 4:7:15$ and Ibrahim has 24 more stickers than Matilda

1. Difference in parts: $15 - 7 = 8$ parts
2. Value of one part: $24 \div 8 = 3$
3. Multiply each person's parts by 3: $12:21:45$

True or false? If the same number of counters is added to both colours in a bag where red : blue $= 3:5$, the ratio is still $3:5$.

False. Adding the same amount to each part changes the ratio; only multiplying both parts by the same number gives an equivalent ratio.

True or false? The greatest number of batches of a recipe you can make is decided by the ingredient you have the smallest amount of.

False. It is decided by the ingredient that gives the fewest batches when compared with the amount the recipe needs.

What are the steps to find the dimensions of a rectangle from a ratio and its perimeter?
e.g. length : width $= 3:1$ and the perimeter is 32 cm

1. Perimeter in parts: $3 + 1 + 3 + 1 = 8$ parts
2. One part: $32 \div 8 = 4$ cm
3. Length $= 3 \times 4 = 12$ cm, width $= 4$ cm

True or false? If there are twice as many blue cubes as yellow cubes, then blue : yellow $= 2:1$.

True.
"Twice as many blue" means for every 1 yellow there are 2 blue, so blue : yellow $= 2:1$.

What are the steps to find a ratio when the quantities are linked by equations?

e.g. $n = 2m$ and $p = 5n$ — find $m : p$

1. Choose the simplest value for the first quantity: $m = 1$.
2. Substitute through the equations: $n = 2$, so $p = 5 \times 2 = 10$.
3. Write the ratio asked for: $m : p = 1 : 10$.